In cases where you are unsure of what hand to use, use your best judgment. Most of the time the top staff is played by the right hand and the bottom staff is played by the left hand. (I specify top/bottom staff because both staves could be written in bass or treble clef).
Sometimes both hands play off of one staff and there are no rests written on the opposite staff. In this case, stem direction usually indicates RH and LH.
Stem direction can give hints as to voicing, so don't always rely on it for which hand. For example, fugues are usually written with each voice in a certain direction. You could have 2 parts in one hand and another 2 parts in the other hand. So don't always rely on stem direction.
When you aren't sure how to play something, try it different ways and see what way is the most comfortable to play.